Panama is a city in Shelby County, Iowa, United States. The population was 235 at the time of the 2020 census. Panama had its start in the y…Panama is a city in Shelby County, Iowa, United States. The population was 235 at the time of the 2020 census. Panama had its start in the year 1882 by the building of the Chicago, Milwaukee and St. Paul Railway through Washington Township.